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arXiv · 2610.38073

Determining norm-Euclidean complex cubic fields

Gustav Kjærbye Bagger·Andrew R. Booker·Tim Trudgian
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Abstract

We prove that Cavallar and Lemmermeyer's list of $58$ norm-Euclidean complex cubic fields is complete. The proof combines a classical discriminant bound with exact certificates of non-Euclideanity. The unit action reduces their verification to finite lattice enumeration with rigorous interval arithmetic. An independent covering computation confirms norm-Euclideanity for the $58$ fields.

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Gustav Kjærbye Bagger, Andrew R. Booker, Tim Trudgian. 2026-10-27. Determining norm-Euclidean complex cubic fields. https://arxiv.org/abs/2610.38073

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